A Historical Welfare Analysis of Social Security: Whom Did the Program Benefit?

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. A Historical Welfare Analysis of Social Security: Whom Did the Program Benefit? William B. Peterman and Kamila Sommer 2015-092 Please cite this paper as: Peterman, William B., and Kamila Sommer (2015). “A Historical Welfare Analysis of Social Security: Whom Did the Program Benefit?,” Finance and Economics Discussion Series 2015-092. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2015.092r1. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

A Historical Welfare Analysis of Social Security: Whom Did the Program Benefit?∗ William B Peterman Kamila Sommer Federal Reserve Board of Governors† Federal Reserve Board of Governors‡ December 7, 2015 Abstract A well-established result in the literature is that Social Security reduces steady state welfare in a standard life cycle model. However, less is known about the historical effects of the programonagentswhowerealivewhentheprogramwasadopted. InacomputationallifecyclemodelthatsimulatestheGreatDepressionandtheenactmentofSocialSecurity,thispaper quantifiesthewelfareeffectsoftheprogram’senactmentonthecohortsofagentswhoexperiencedit. Incontrasttothestandardsteadystateresults,wefindthattheadoptionoftheoriginal Social Security tended to improve these cohorts’ welfare. In particular, we estimate that the originalprogrambenefitedhouseholdsaliveatthetimeoftheprogram’sadoptionwithalikelihood of over 70 percent, and increased these original agents’ welfare by the equivalent of 3.5%oftheirexpectedfuturelifetimeconsumption. Thewelfarebenefitwasparticularlylarge for poorer agents and agents who were near retirement age when the program was enacted. Through a series of counterfactual experiments we demonstrate that the difference between the steady state and transitional welfare effects is primarily driven by a slower adoption of payrolltaxesandaquickeradoptionofbenefitpaymentsduringtheprogram’sphase-in. Overall, the opposite welfare effects experienced by agents in the steady state versus agents who experienced the program’s adoption might offer one explanation for why a program that potentiallyreduceswelfareinthesteadystatewasoriginallyadopted. JEL:E21,D91,H55 KeyWords: SocialSecurity,Recessions,GreatDepression,OverlappingGenerations. ∗ViewsexpressedinthispaperareourownanddonotreflecttheviewoftheFederalReserveSystemoritsstaff. Forpreliminarydiscussionsandhelpfulcomments,wethankKevinNovan,R.AntonBraun,andCarlosGarriga. †20thandCStreetNW,WashingtonDC20551. Tel: 202-452-3703. E-mail: william.b.peterman@frb.gov. ‡20thandCStreetNW,WashingtonDC20551. Tel: 202-452-2909. E-mail: kamila.sommer@frb.gov.

“Wecanneverinsureonehundredpercentofthepopulationagainst onehundredpercentofthehazardsandvicissitudesoflife,butwe havetriedtoframealawwhichwillgivesomemeasureofprotection totheaveragecitizenandtohisfamilyagainstthelossofajoband againstpoverty-riddenoldage.” F.D.RooseveltduringthesigningofTheSocialSecurityActof1935 1 Introduction Social Security was implemented amidst the Great Depression, and represented the largest U.S. social insurance program at the time. While Social Security has been shown to generally mitigate welfarelossesduringdeepeconomicdownturns(PetermanandSommer(2014)),alargeliterature has shown that the current program reduces steady state welfare and also has explored the welfare implicationsofvariousreforms. However,theexistingliteraturehasbeenmostlysilentonwhythe program—given its welfare costs in the steady state—was implemented in the first place. To this end, our paper uses a general equilibrium, heterogeneous-agents life cycle model to quantitatively examine the welfare effects of the Social Security program’s adoption on the original cohorts of agents who experienced it. In particular, we ask three questions. First, what were the overall welfare effects on individuals who were alive at the program’s adoption? Second, who were the winnersandlosersfromtheprogram’senactment? Andthird,whatwerethemainchannelsthrough whichtheadoptionoftheoriginalprogramaffectedwelfare? Weexaminethesequestionsinthreesteps. First,webuildarich,heterogeneousagent,general equilibriumlifecyclemodelwithendogenouslaborandretirementthatmatchestheU.S.economy just before the Great Depression and the enactment of the original Social Security program. Second, we introduce two sudden and unexpected shocks—the Great Depression and the subsequent adoption of the original Social Security—and calculate the transition path to a new, post-Great Depression steady state with Social Security fully phased in. Third, along the transition path, we study the welfare of the original cohorts of agents who lived through the Great Depression and the subsequent enactment of Social Security, and compare it to the welfare of agents who experiencedacounterfactualtransitionpathwheretheGreatDepressionoccursbutSocialSecurityisnot adopted. We measure the welfare effects of the original Social Security in two distinct ways. First, we 1

determine the likelihood of a welfare gain from the adoption of Social Security for these original cohorts and, second, we calculatethe average size of thewelfare gains for agents inthese cohorts. Our quantitative experiments suggest that the original program benefited a vast majority of agents whowerealiveatthetimeoftheprogram’senactment,withtheaveragewelfareeffectbeinglarge and widespread. In particular, we estimate that the original program benefited households alive at the time of the program’s adoption with a likelihood of over 70 percent, and increased these original agents’ welfare by the equivalent of 3.5% of their expected future lifetime consumption. These welfare benefits were particularly large for working-age individuals close to retirement and alsoforagentswithrelativelylesssavings. We find that the welfare benefit from the adoption of the original program can largely be explained by the relative speeds at which the different parts of the program were phased in. In particular, the structure of the original Social Security program meant that many (especially older working)agentswhowerealiveatthetimeoftheprogram’sadoptionreceivedfargreaterbenefits fromSocialSecuritythantheamounttheycontributedtofundit. Forexample,atransitionalagent whoretiredfiveyearsaftertheinceptionofSocialSecuritywouldfacealifetimepayrolltaxburden that was approximately 95 percent lower than that of an agent who lived their whole lifetime with Social Security, largely because this transitional agent would only pay payroll taxes for five years insteadofhiswholeworkinglifetime.1 However,becauseofhowthebenefitswerephasedin,this transitionalagentwouldbeentitledtoaSocialSecuritybenefitthatwasonly40percentlower. Interestingly, and perhaps counter to simple intuition, we find that adopting the program during the Great Depression in fact tapered the welfare benefits from the program for the original cohorts. At first blush, one might be tempted to think that the Great Depression could have bolstered the welfare gains because the insurance from the Social Security benefits would be more valuableduringtheGreatDepressionwhenlargeamountsofwealthandincomewerelost. Onthe other hand, imposing a payroll tax on agents during the Great Depression when agents suffered from tighter budget constraints due to the adverse shock could lower the welfare gains from the program’s adoption. On balance, we find that this latter channel dominates because most agents who were eligible for Social Security did not receive Social Security benefits for many years to 1This calculation also includes the effects of a lower payroll tax rate faced by this agent because the payroll tax ratewasscaleduptoitssteadystatevalueoveranumberofyears. 2

come,buthadtostartfundingthesystemimmediately. This paper is related two strands of literature that examine the effect on welfare of Social Security. The first strand tries to measure the steady state implications on welfare of Social Security. Theseworksweightherelativebenefitfromprovidingpartialinsuranceforrisksinwhichnomarketoptionexistsagainstthewelfarecostsofdistortinganindividual’sincentivestoworkandsave. Thesestudies—whichlargelyfocusonthebenefitofprovidingintra-generationalinsuranceforidiosyncraticearningsandmortalityrisksincludeAuerbachandKotlikoff(1987),HubbardandJudd (1987), Hubbard (1988), Imrohoroglu et al. (1995), Fuster et al. (2007), Storesletten et al. (1998), and Hong and R`ıos-Rull (2007).2 Moreover, Krueger and Kubler (2006) and Harenberg and Ludwig (2013) examine the steady state welfare implications of Social Security with a moderate level ofaggregaterisk,designedtoweightheinter-generationalinsurancebenefitsfromSocialSecurity against the program’s economic costs. By and large, the studies find that Social Security is not welfare improving: the insurance benefits from Social Security are outweighed by the distortions that the program imposes.3 Similar to these papers, we aim to examine the welfare consequences ofSocialSecurity. However,thisstudyisdifferentinthatitfocusesonthewelfareimplicationsof the Social Security program over the transitional period after the program is adopted, as opposed to focusing on the steady state welfare effects of the program once it is well established. Overall, our findings that the welfare effects of Social Security are the opposite for agents in the steady state versus agents who experienced the program’s adoption might offer one explanation for why a program that potentially reduces welfare in the steady state was originally adopted. In addition,totheauthors’knowledge,thisisthefirstlifecyclemodelcalibratedtoanalyzethehistorical episode of the Great Depression that includes endogenous retirement, endogenous labor supply, andidiosyncraticearningsrisk. Similar to this paper, a second strand of the literature focuses on the transitional welfare as opposedtothesteadystatewelfareimplicationsofSocialSecurity. However,insteadofexamining the welfare implications of adopting Social Security, this strand of the literature analyzes either the welfare implications of reforming Social Security or the implications of the program during 2ForatheoreticaldiscussionofthedifferenttypesofrisksthatSocialSecuritycanprovideinsuranceagainstsee Shiller(1998). 3OneexceptionisImrohorogluetal.(2003),whichfindthatifpreferencesaretime-inconsistentthenthebenefits ofSocialSecurityoutweighthecosts. 3

a particular business cycle episode. For example, Peterman and Sommer (2014) shows that Social Security mitigated a notable amount of the potential welfare losses from the Great Recession, particularly for poorer and older agents. Examples of studies that assess the transitional welfare implications of reforming Social Security include: Olovsson (2010), Imrohoroglu and Kitao (2012), Kitao (2012), Huggett and Parra (2010), and Huggett and Ventura (1999). These papers generally find that although reforms to Social Security will increase steady state welfare, welfare decreases during the transition. In the spirit of both of these types of papers, we determine the transitionalwelfareeffectsonlivingagents. However,weexaminethewelfareimplicationsduring a transitional period that includes the implementation of Social Security, rather than a reform or a phase-outofanalreadyexistingprogram. This paper is organized as follows: Section 2 introduces the computational model. Section 3 presentsthedynamicprogrammingproblem. Section4describesthefunctionalformsandcalibration parameters. Section 5 describes the computational experiment. Section 6 reports the results ofthecomputationalexperiment. Section7concludes. 2 Model Our framework is a general equilibrium, life cycle economy with overlapping generations of heterogeneous agents, uniquely built and calibrated to quantify the welfare effects of the adoption of theoriginalSocialSecurityprogramonagentswhowerealiveattheprogram’sadoption. TheinitialsteadystateiscalibratedtotheU.S.economypriortotheGreatDepressioninwhichnoSocial Securityexists. WethenintroducetheGreatDepression,afterwhichtheeconomytransitionsona perfect foresight path. However, this path is altered by a second unexpected shock, the introduction of Social Security. Thus, the final steady state represents the U.S. economy after a transition through the Great Depression and the adoption of Social Security in accordance with historical law.4 4WefocusonthewelfareeffectsoftheoriginalSocialSecurityprogramthatwasimplementedbetween1938and 1940andthuswedonotincorporateanysubsequentchangestogovernmentprograms. 4

2.1 Demographics Time is assumed to be discrete, and the model period is equal to one year. Agents enter the model when they start working at age 20. Agents can live to a maximum possible age of J. Thus, in each period, the economy is populated by J−19 overlapping generations of individuals of ages 20,21,...,J. The size of each new cohort grows at a constant rate n. Lifetime length is uncertain, with mortality risk rising over the lifetime. The conditional survival probability from age j to age j+1 is denoted Ψ where Ψ =0. Annuity markets do not exists to insure life-span uncertainty j J andagentsareassumedtohavenobequestmotive. InthespiritofConesaetal.(2009),accidental bequests,whicharisefromthepresenceofmortalityrisk,aredistributedequallyamongsttheliving in the form of transfers Tr . Agents endogenously choose the age j =R at which the retire. The t binarydecisiontoretire(i.e.,I ={0,1}whereI =1denotestheeventofretirement)isconsidered irreversibleandisrestrictedtobewithintheagerangeof[R,R]. 2.2 Endowments, Unemployment, Preferences and Market Structure In each period t, an agent is endowed with one unit of time that can be used for leisure or market work. An agent’s labor earnings are given by y = w ω h (1−D ), where w represents the t t t t t t wage rate per efficiency unit of labor, h is the fraction of the available time endowment spent on t labor market activities, D is the fraction of the time endowment in each period that the agent is t exogenously unemployed, and ω is the idiosyncratic labor productivity which follows the prot cess: logω = θ +α+ν . In this specification, θ , which is deterministic, governs the average t j t j age-profile of wages (or age-specific human capital), α ∼ NID(0,σ2) is an individual-specific α fixedabilityshock thatisobservedwhenan agent enterstheeconomyandstays fixedforanagent over the life cycle, and ν is a persistent shock, received each period, which follows a first-order t autoregressiveprocess: ν =ρν +ψ ,withψ ∼NID(0,σ2)andν 0=0.Theexogenousunemt t−1 t t ν 2 ployment shock, D , is discretized to two values, zero and d ∈(0,1]. The positive value d, which j indicates an unemployment spell, arrives with a probability pU. When the unemployment spell hits,theagentlosestheoptiontoworkduringd percentoftheirtimeendowment. Agent’s preferences over the stream of consumption, c, and labor supply, h, are governed by a time-separableutilityfunction: E 2 0∑ J j=20 βjU(c j ,h j ,I j ),whereβisthediscountfactorandwhere 5

theexpectationistakenwithrespecttothelife-spanuncertainty,theidiosyncraticlaborproductivity process, and the unemployment process. The period utility function, U(c ,h ,I ), is modeled j j j as the weighted average of the utility from the sub-period in which an agent is employed and the sub-period in which the agent is unemployed: U(c ,h ,I )=(1−D )u(c ,h ,I )+D u(c ,0,I ). j j j j j j j j j j Modeling the per-period utility function as the weighted average of the utility flows from the two sub-periodsallowsustopickarelativelylonger,computationallymoretractablemodelperiod(one year),butstillincorporateunemploymentspellsthatareshorterthanoneyear.5 Agents can hold savings in the form of assets, a ≥0. Agents choose to save for two reasons. j First, they save to partially insure against idiosyncratic labor productivity, unemployment, and mortalityrisks. Moreover,theysaveinordertohelpfundtheirpost-retirementconsumption. Once SocialSecurityisadopted,theprogramprovideanothersourceofpost-retirementconsumption. 2.3 Technology Firms are perfectly competitive with constant returns to scale production technology. Aggregate technology is represented by a Cobb-Douglas production function of the formY =F(A,K,N)= AKζN(1−ζ), where A, K, N, and ζ are aggregate Total Factor Productivity (TFP), capital, labor, and the capital share of output, respectively. Capital depreciates at a constant rate δ∈(0,1). The firms rent capital and hire labor from agents in competitive markets, where factor prices r and w t t are equated to their marginal productivity. The aggregate resource constraint is: C +K −(1− t t+1 ζ 1−ζ δ)K +G ≤ AK N where, in addition to the above described variables, C and G represent t t t t t t aggregateindividualandgovernmentconsumption,respectively. 2.4 Government Policy The government distributes accidental bequests to the living in a form of lump-sum transfers, Tr , t and consumes in an unproductive sector.6 Government consumption, G , is exogenously detert mined, and is modeled as proportional to the total output in the steady state economy, so that 5We make the additional assumption that consumption is constant within the sub-periods. Since we use a utility functionthatisseparableinconsumptionandhoursworked, theconstantconsumptionassumptionisnotbindingas longastheagentrealizesD atthebeginningoftheperiodandcanparticipateinintra-periodborrowing. j 6By the timing convention, agents realize at the beginning of the period whether they die. Subsequently, the transfersarereceivedatthebeginningoftheperiodbeforeagent’sidiosyncraticlaborproductivitystatusisrevealed. 6

G =φY. ThelevelofgovernmentspendingisdeterminedinthesteadystatewithoutSocialSecut t rityandisheldconstantthroughoutthetransition. OnceSocialSecurityisenacted,thegovernment additionally collects a proportional Social Security tax, τss, on pre-tax labor income of workingt age individuals (up to an allowable taxable maximum y) to finance Social Security payments, bss, t forretiredworkers. ThegovernmenttaxesincomeaccordingtoascheduleT(y˜)inordertoraiserevenuetofinance t its spending in the unproductive sector. The taxable income, y˜, is defined as: y˜ = y +r (Tr + t t t t t a )−0.5τssmin{y ,y }. The part of the pre-tax labor income (y ) that is accounted for by the t t t t t employer’s contributions to Social Security (0.5τssmin{y ,y }) is not taxable. In the benchmark t t t steadystatewithnoSocialSecurity,τss issettozero. t Similar to the current system, the original Social Security benefits were calculated as an increasing,concave,piecewise-linearfunctionofworker’saverageleveloflaborearnings. However, the original program was considerably less progressive, with the benefits formula being governed byasinglebendpointandtwomarginalreplacementrates. Unlikethecurrentprogram,theoriginal Social Security benefits were adjusted for the number of years in which an individual contributed payrolltaxesandthebenefitsweredisbursedonlyafteranagentreachedthenormalretirementage (NRA)of65.7 SocialSecuritypaymentsarecomputedusingequation: Jr bss = f(x )×(1+ ), (1) j 100 and are calculated in three steps. First, we compute each worker’s average level of labor earnings over the working life cycle, x . At every age, the total accumulated earnings follow the law of j=R motion: min{y ,y}+(j−1−19)x j j x = , (2) j+1 j−19 where x is the accounting variable capturing the equally-weighted average of earnings before the j retirement age J ; and y is the maximum allowable level of labor earnings subject to the Social r 7The current system has two bend points and three marginal replacement rates. Moreover, it allows individuals to claim Social Security benefits, though actuarially adjusted, prior to reaching their NRA. Finally, there are no adjustments to the Social Security benefits for the number of years worked, only the top thirty years of income are considered,andearnedincomeonlythroughage70isfactoredintothecalculationoftheSocialSecuritybenefit. For adetailedreviewofthecurrentsystem,seePetermanandSommer(2014). 7

Security tax that corresponds to the benefit-contribution cap.8 Second, the pre-adjustment Social Security benefit, bss = f(x ), for each retiree is calculated using a convex, piecewise-linear base j=R functionofaveragepastearningsobservedatretirementage,x ,sothatthemarginalbenefitrate j=R variesoverthreelevelsoftaxableincome: τ for 0≤x <b r1 R 1 τ for b ≤x <b (3) r2 1 R 2 0 for x ≥b . R 2 The parameter b is the first bend point, b is the benefit-contribution cut-off point (b =y), and 1 2 2 {τ ,τ } represent the marginal replacement rates for the pre-adjustment Social Security benefit. r1 r2 Finally, an adjustment is made to the benefits to account for the number of years of payroll tax contributions. In particular, in a departure from the current system, for each year that agents pay payrolltaxes,theirbenefitsarescaledupbytheequivalentofonepercent,inlinewiththeoriginal program. As a result, the total Social Security benefit bss obtained by the retiree is defined as: bss =bss ×(1+ R )withbss ∈[bss ,bss ]. base 100 min max 3 Dynamic Program and Definition of Equilibrium For expositional convenience, this section introduces the dynamic program of an individual who enters the economy in the final steady state with Social Security. The program simplifies into the problem solved in the initial steady state economy with no Social Security once τss and bss are set tozero. TheAppendixprovidesaformaldefinitionofthemarketequilibrium. 8IfanagentchoosestoretirepriortotheNRA,thentheiraverageearningsfornon-workingyearspriortoreaching theNRAarepopulatedwithzero. Additionally, ifanagentchoosestoworkpasttheNRAthentheadditionalyears workedpasttheNRAarefactoredintotheirlifetimeaverageearningsfromwhichtheultimateSocialSecuritybenefits arecomputed. 8

3.1 Dynamic Program of a Previously Working Agent An agent who was working in the previous period and is indexed by type (a ,x ,α,ν , j,D) solves t t t thedynamicprogram(suppressingtimesubscripts):   max c,a(cid:48),h U(c,h,D)+βs j EV t+1 (a(cid:48),x(cid:48),α,ν(cid:48),j+1,D(cid:48)) if j≤R, V(a,x,α,ν,j,d)= (4) t  max U(c,h,D)+βs EV (a(cid:48),x(cid:48),α,,ν(cid:48),j+1,D(cid:48)) if R< j≤R, c,a(cid:48),h,I={0,1} j t+1 subjectto c+a(cid:48)=(1+r)(Tr+a)+y−T(y˜)−τssmin{y,y} if I=0, (5) c+a(cid:48)=(1+r)(Tr+a)−T(y˜)+bss if I=1. by choosing consumption, c>0, savings, a(cid:48) ≥0, the fraction of available time endowment spent onworking,h,andwhethertopermanentlyretire,I∈{0,1}. Agentsearninterestincomer(Tr+a) on the lump-sum transfer, Tr, from accidental bequests and on asset holdings from the previous period, a. y represents the pre-tax labor income of the working agents and y˜ defines the taxable income on which the income tax, T, is paid. D∈{0,d} is the state variable for the fraction of the periodanagentisexogenouslyunemployed. TheSocialSecuritytaxrate,τss,isappliedtothepretaxlaborincome,y,uptoanallowabletaxablemaximum,y,andbss denotestheindividual-specific constant Social Security benefit that is received by retired agents every period after reaching the NRA. 3.2 Dynamic Program of a Previously Retired Agent Retired agents are no longer affected by labor productivity or unemployment shocks because they nolongerwork. Assuch,aretiredagentsindexedbytype(a ,bss, j)solvesthedynamicprogram: t V(a,bss, j)=maxU(c,h)+βs EV (a(cid:48),bss, j+1), (6) t j t+1 c,a(cid:48) subjectto c+a(cid:48) =(1+r)(Tr+a)+bss−T(y˜), (7) by choosing consumption, c, and savings, a(cid:48). Similarly to non-retired agents, retirees earn interest income r(Tr+a) on the transfer, Tr, and their existing asset holdings, a. These agents who are 9

older than the NRA also receive the constant per-period Social Security payment, bss, one the programisimplemented. 4 Calibration of the Steady States We begin by calibrating the initial steady state that excludes Social Security. Thus, to the extent that reliable data are available, we use historical data prior to the adoption of the original Social SecurityprogramtocalibratetheinitialsteadystatemodelwithnoSocialSecurity. Whenavailable, parameter values are taken directly from the data. The remaining parameters in the model are set such that the model reproduces key historical moments of the U.S. data. After calibrating the benchmarkeconomywithoutSocialSecurity,weparametrizetheoriginalSocialSecurityprogram and compute the final steady state while keeping all the non-Social Security parameters at their levelsinthebenchmarkmodel. AlltheparametersvaluesaresummarizedinTable1. 4.1 Demographics, Endowments, Unemployment risk and Preferences There are 74 overlapping generations of individuals of ages j =20,...,93. The population growth rate, n, is set to 1.6 percent to match the average U.S. annual population growth (reported by the Census Bureau) from 1920 through 1928. The conditional survival probabilities, Ψ , are derived j from the U.S. life tables for the 1930s (Bell and Miller (2002)). To increase the computational tractability of the model, the minimum and maximum ages at which an agent is allowed to retire (RandR)inthemodelaresetat60and85,respectively.9 Ideally, to calibrate the wage process, we would rely on panel data on wages. However, such historical data are not available. Given the lack of data, we follow Conesa et al. (2009) in calibratingtheprocessforthelaborproductivity,ω,basedoncross-sectionalwagedatafromthe1940 Census.10 We restrict the estimation sample to male household heads who were between ages 20 9Constrainingthebinaryretirementdecisionsto25yearsreducesnumberofperiodsinwhichsuchdecisionsare made,therebyreducingthestatespace. Thatsaid,disallowingagentsfromretiringpriortoage60inthemodeldoes not seem to be inconsistent with the data, as less than 10 percent of all male household heads were reported out of laborforceineitherthe1920orthe1930Census(i.e.,inaperiodpriortotheadoptionoftheoriginalSocialSecurity program). 10Ideally,theproductivityprocesswouldbecalibratedfromdatapriortotheGreatDepressionandtheimplementationofSocialSecurity. Unfortunately,tothebestofourknowledge,suchdataarenotreadilyavailablepriorto1940. ToreducetheeffectsoftheadoptionofSocialSecurityin1940onourestimates,ouranalysisfocusesonobservations 10

Table1: CalibrationParametersinSteadyState Parameter Value Source/Target Demographics: NormalRetirementAge: NRA 65 U.S.SSProgram MinimumRetirementAge: R 60 ByAssumption MaximumRetirementAge: R 85 ByAssumption MaxAge: J 93 ByAssumption Surv. Prob: Ψ BellandMiller(2002) j Pop. Growth: n 1.6% Conesaetal.(2009) FirmParameters: ζ .36 Data δ 6.90% I =25.5% Y A 1 Normalization PreferenceParameters: ConditionalDiscount: β∗∗ 0.9845 K =3.0 Y Riskaversion: γ 2 Conesaetal.(2009) FrischElasticity: σ 0.5 Data;IntensiveFrisch= 1 2 DisutilitytoLabor: χ∗∗ 67.2 Avg. h =.282 1 j FixedCosttoWorking: χ∗∗ 0.344 14.3%retiredatage65 2 ProductivityParameters: PersistenceShock: σ2 0.007 1940Census ν Persistence: ρ 0.990 1940Census PermanentShock: σ2 0.437 1940Census α UnemploymentRate: p 4.1% Data d UnemploymentDuration: d 0.30 Palmer(1937) GovernmentParameters: ϒ∗∗∗ .059 MrktClearning 0 ϒ∗∗∗ .298 .5Avg. Earnings 1 φ 2.8% Data SocialSecurity: τ 40% U.S.SSProgram r1 τ 10% U.S.SSProgram r2 b∗∗ .57xAvgEarnings U.S.SSProgram&NBER 1 y∗∗∗ 2.84xAvgEarnings U.S.SSProgram&NBER bss∗∗∗ 0.11xAvgEarnings U.S.SSProgram&NBER min bss∗∗∗ 0.97xAvgEarnings U.S.SSProgram&NBER max τss∗∗∗ 4.45% MrktClearing Note: ∗∗denotesparameterseithercalibratedthroughtheMethodofSimulatedMomentsorweredeterminedinequilibriumthroughmarketclearing.∗∗∗denotesparametersbasedoffofaggregatesthataredeterminedintheequilibrium. 11

Figure1: DeterministicAgeProfileofWages 2.5 2 1.5 1 0.5 0 20 30 40 50 60 70 80 ytivitcudorP Age and 64, worked at least five weeks, and worked more than 1,248 hours over the year. To pin down the deterministic age-specific productivity profile, we regress natural log of average wages on a quadraticpolynomialofage,andnormalizetheexponentialtransformationofthisprofiletooneat age 20. This exponential transformation is shown in Figure 1. Having calibrated the deterministic age-profile, we next use the age-specific variance of the natural log of wage by age (shown in Figure 2) to infer the parameter values for the permanent and persistent shocks to the individuals’ productivity. First, we set the variance of the permanent shock, σ2, to 0.437 in order to match the α minimumvarianceofthenaturallogofwagesbetweenages20and30inthedata. Second,turning to the persistent productivity shock, we set ρ=0.990 to match the linear growth of the variance in wages over the life cycle, depicted by the solid line in Figure 2. Finally, we set σ2 so that its ν calibrated value minimizes the sum of squared percentage deviations between the empirical and simulated variance of wages at each age (plotted in Figure 2). In order to solve the model, we discretizethepermanentandpersistentshockwithtwoandfivestates,respectively.11 To calibrate the unemployment shock we rely on the data from the Philadelphia Labor Survey (Palmer (1937)), a historical survey of the Philadelphia labor market from 1929 to 1937. Using the 1929 data, we calibrate the unemployment shock D∈{0,d =0.3}, so that prior to the Great Depression unemployed agents spend thirty percent of the year unable to work. Turning to the probability of an unemployment shock, we set p = 0.041 to match the national average unemd forindividualswhowereyoungerthantheNRAin1940. However, weareunabletocontrolfortheeffectsthatthe adoptionofSocialSecuritymighthavehadonlaborsupplyandwagewagedynamicsofyoungerindividuals. 11Giventhehighlypersistentprocess,weusetheRouwenhorstmethodtodiscretizetheproductivityprocess. 12

Figure2: UnconditionalVarianceofNaturalLogofWages 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 20 30 40 50 60 sgninraE nL fo ecnairaV Data Predicted Age ploymentrateovertheperiod1945-1950intheNBERunemploymentseries.12 AsdiscussedinSection2.2,theper-periodutility,U(c,h,I),ismodeledastheweightedaverage betweentheutilityflowsfromthesub-periodinwhichtheagentisunemployedandthesub-period in which the agent is employed.13 We model the preferences within each sub-period as additively separablebetweenconsumption(c)andlabor(h): 1−γ 1+1 c h σ u(c ,h ,I )= it −χ it −χ (I −1), (8) it it it 1−γ 1 1+ 1 2 it σ where γ > 0, σ > 0, χ > 0, χ > 0, and I is an indicator for whether an agent is retired. The 1 2 constantrelativeriskaversionpreferencesoverconsumptionarecharacterizedbytheriskaversion coefficient, γ, which determines an agent’s desire to smooth consumption across time and states. The existing estimates of γ (though generally based on more recent data) typically range between 1and3. Giventhelackofhistoricalestimates,wesetγ=2. The parameter σ represents the Frish labor supply elasticity on the intensive margin. Past microeconometricstudiesestimatetheFrischelasticitytobebetween0and0.5.14 However,more 12The NBER series compiles estimates from several different sources. The 1929-1944 estimates are based on Conference Board data, whereas the 1945-1946 estimates are from Census Bureau’s “Current Population Reports.” Finally, the estimates from 1947-1950 are from U.S. Bureau of Labor Statistics’s “Employment and Earnings and Monthly Report on the Labor Force.” See http://www.nber.org/databases/macrohistory/contents/chapter08.html for moredetails. Theaverageestimateforthe1945-1950periodisfairlyclosetotheavailableestimatesfor1929ofabout 3percentfromDarby(1975)andLebergott(1964). 13IfD=0thenanagentisalwaysemployedandonlyonesub-periodisincluded. 14See,forexample,Kaplan(2012),Altonji(1986),MaCurdy(1981),DomeijandFloden(2006)orBrowningetal. 13

recent research shows that these estimates may be biased downward.15 Again, given the lack of historicalestimates,wecalibrateσto0.5—theupperrangeoftheavailableestimates. Turningtotheremainingpreferenceparameters,thescalingconstantχ iscalibratedsuchthat, 1 agentsspendonaverage28.2percentoftheirtimeendowmentworkingpriortoreachingtheNRA, correspondingtothe1940Censusinwhichmalehouseholdheadsworkedonaverage1,760hours per annum.16 Additionally, consistent with the 1930 Census, the fixed cost of working, χ , is 2 calibrated so that 14.3 percent of male head of households retire by the NRA.17,18 Finally, the discount factor, β, is calibrated to 0.9845 to endogenously match the U.S. capital-to-output ratio of3.0.19 Given the number of simplifying assumptions due to the lack of historical data, it is helpful to compare the endogenously generated retirement decisions in the baseline model against the available historical estimates. Figure 3 plots the fraction of male household heads age 60+ who are not in the labor force in the data against the fraction of retired agents in the model’s initial steady state without Social Security. Even though we only directly target the fraction of retired households at age 65 (14.3 percent) in the calibration, the average retirement decisions across the wholeagerangegeneratedbythemodellookremarkablysimilartothedata. 4.2 Firm The aggregate production function is Cobb-Douglas, with the capital share parameter, ζ = 0.36. The depreciation rate is calibrated such that the investment to output ratio is 25.5 percent, as reportedbytheBEAin1929and1930. (1999). 15SeeImaiandKeane(2004),DomeijandFloden(2006),Pistaferri(2003),Chetty(2009),ContrerasandSinclair (2008),andPeterman(Forthcoming). 16IdeallyhourswouldbecalibratedtothedatapriortotheimplementationofSocialSecurity. However,hoursdata arenotavailablefromtheCensusuntil1940.InordertogetaroundtheeffectsofSocialSecurityonhours,wecalibrate tohoursworkedforindividualswhoaretooyoungtobeeligibletocollectSocialSecuritybenefits. 17GiventhattheCensusdataforthisperioddoesnotdirectlyreportretirementstatus,individualswhoarenotinthe laborforceintheCensusdataareconsideredretired. Thisassumptionseemsreasonableforyoungeragentssinceless thanfivepercentofheadsofhouseholdsundertheageof55arenotinthelaborforceintheCensusdata. 18Thefixedcostχ >0impliesthatthedisutilityfromworkingdiscontinuouslyincreaseswhenanagentgoesfrom 2 zerotopositivehoursworked. SeePetermanandSommer(2014)foradiscussionofthismodelingapproachusedina similarframework. 19CapitaliscalculatedasthesumofprivatefixedassetsandconsumerdurablesreportedbytheBureauofEconomic Analysis. Thevaluesarenotreportedpriorto1929. However,theratioiscenteredaround3from1929through1931. 14

Figure3: PercentRetired 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 60 65 70 75 80 85 deriteR tnecreP Data (1930) Model (No Social Security) Age Note: The data are from the 1930 Census. We limit the sample to males who are head of their household. Given thattheCensusdataforthisperioddoesnotdirectlyreportretirementstatus, inthedata, individualswhoarenotin thelaborforceareconsideredtoberetired. Themodelcapturesthepercentofretiredindividualsinthesteadystate withoutSocialSecurity. 4.3 Government Government spending in the unproductive sector, φ, is set to 2.8 percent of GDP, consistent with theratioofFederalGovernmentexpenditurestoGDPreportedbytheBEAin1929and1930. Turningtotheincometaxfunction,inthe1930s,thefederaltaxpolicywasmuchlessprogressive than the current system. In particular, a large fraction of taxable income was tax-exempt, and the rest was taxed at a low marginal flat rate of 4 percent for most individuals.20 Consequently, closeto50percentoftaxreturnshadzeroornegativetaxliabilityinthe1930s.21 Thus,wemodel thestylizedincometaxpolicyas: T(y˜;ϒ ,ϒ )=ϒ max{y˜ −ϒ ,0}, (9) t 0 1 0 t 1 whereϒ istheflatmarginaltaxrateandϒ controlsthelevelofthetaxexemption. ϒ iscalibrated 0 1 1 sothat50percentoftaxfilersdonotpayanytaxesintheinitialsteadystate. Moreover,wecalibrate 20The first $2,500 of income for married households and $1,000 for single filers was tax-exempt. Moreover, the marginal tax rate for the part of the first $4,000 of income that was not exempt was flat at four percent, and then increased only very gradually for higher income. These exemption levels and the limit on the first tax bracket were quitehighcomparedtothemeanincomeof$1,054in1929(calculatedfromtheMacroeconomichistoricaldatafrom theNationalBureauofEconomicResearch). 21Source: TaxFoundation(http://taxfoundation.org/article/federal-individual-income-tax-returns-zero-or-negativetax-liability-1916-2010) 15

ϒ suchthatthegovernmentbudgetconstraintclears. Wefindthatthemarginalrateof5.94percent 0 clears the government’s budget, implying an average tax rate of 3.5 percent. This rate is generally consistent with the average historical income tax rates listed in Table 2, which varied between 2.6 and4.3percentfrom1923-1930. Table2: AverageIncomeTaxRates Year Rate 1923 2.6% 1924 2.7% 1925 3.3% 1926 3.3% 1927 3.5% 1928 4.3% 1929 3.8% 1930 2.8% Notes: Thevaluesarecalculatedastheratioofthetotalincometototaltaxliability. ThedataarefromtheTaxPolicy Center. Inaccordancewiththehistoricallaw,wesettheNRAto65andsetmarginalreplacementrates (τ ,τ ) to their respective values in the data of 0.4 and 0.1.22 Similarly, in the spirit of Huggett r1 r2 and Parra (2010), we set the bend point (b ), the maximum earnings (y), the maximum benefit 1 (bss ), andthe minimumbenefit (bss ) sothat theyoccur at0.57, 2.84, 0.97, and0.11 timesmean max min earningsintheeconomy.23 5 Calibration of the Transition Path Having calibrated the initial and final steady states, this section parameterizes (i) the economic shocks associated with Great Depression and (ii) the phase-in of the original Social Security program as the economy transitions from the initial steady state without Social Security to the final steady state with Social Security. Both the Great Depression and the phase-in of Social Security 22Thesereplacementratesweresetinthe1939amendment. Intheoriginallawtheprogramsparameterswereless progressiveandmoreheavilydependentonthenumberofyearsanindividualworked. 23Seehttp://www.nber.org/databases/macrohistory/contents/. 16

Figure4: Timeline TFP & unemp. shocks TFP & unemp. shock persists (follow data) persists (extrapolate) dne skcohS areincorporatedinthemodelconsistentwiththeactualhistoricalexperience. Figure4outlinesthe timelineoftheseeventswhicharediscussedinthesubsequentsections. 5.1 The Great Depression We model the initial unexpected economic downturn associated with the Great Depression as one thataffectstheeconomythroughthreedistinctchannels: anadverseTFPshock,anadversecapital depreciation shock, and an adverse unemployment shock. We calibrate these shocks to match the totalchangesintheavailableempiricalestimatesoftheTFP,capitalstockandunemploymentrate between 1929 and 1932 (see timeline in Figure 4).24 After these initial sudden and unexpected shocks, we model the rest of the Great Depression through elevated unemployment risk and depressedTFPthatpersistthrough1945. Unliketheinitialshocks,thesepersistentaggregateshocks after1932arenolongertreatedasasurprise. Figure 5 shows the 1890-1950 historical estimates of TFP from Kendrick et al. (1961). With 24Forcomputationalconvenience,theinitial1929-1932changesinTFP,capitalstockandunemploymentarecondensedintoasingleperiod. 17

Figure5: TotalFactorProductivity 160 140 120 100 80 60 40 20 0 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 xednI Year Note: The solid black line is TFP reported in Kendrick et al. (1961). The dashed red line is predicted TFP using a regressionthatexcludesthedummyforyearsduringGreatDepression. the exception of the Great Depression, Kendrick’s TFP series is generally increasing throughout the first half of the 20th century. In order to isolate the change in TPF (or the TFP shock) due to the Great Depression, we control for the observed time trend by regressing Kendrick’s TFP series on a third order polynomial in time and a binary indicator for the Great Depression (1930-1940). ThereddashedlineinFigure5depictsthepredictedTFPfromtheregression(excludingtheeffect of the indicator variable for the Great Depression). For every year between 1930 and 1940, we define the TFP shock associated with the Great Depression as the difference between the actual TFP (black line) and the predicted counterfactual TFP (red dashed line) that excludes the effects of the Great Depression. After 1940, one complicating factor of our analysis is the presence of the economic effects associated with World War II (WWII) that were probably not anticipated at the time when Social Security was adopted.25 To exclude the extra boost to TFP from WWII, we assume that instead of recovering immediately, TFP linearly recovers to its expected 1945 value fromits1940valueoverthenextfiveyears. Turning to the capital depreciation shock, according to the BEA, the value of fixed assets fell by 24 percent between 1929 and 1932. We implement this shock with a one-time increase of 24 percentage points to the depreciation rate, δ. This one-time increase in δ is assumed to be unexpected and immediately dissipates, though its effects on the economy persist as it takes time 25AlthoughtheUnitedStatesdidnotenterthewaruntillater, productionforwaractivitiesaboardincreasedprior totheU.S.enteringthewar. 18

Figure6: UnemploymentDuringGreatDepression 30% 25% 20% 15% 10% 5% 0% 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 etatR tnemyolpmenU Conference Board Lebergott Darby Year Note: ThesolidblacklinearetheaveragemonthlyestimatesfromtheConferenceBoardpublishedinMoore(1961). ThedashedbluelinearetheestimatesfromLebergott(1964)whichconsidersindividualsin“workrelief”asunemployed. The dashed blue line are the estimates from Darby (1975) which considers individuals in “work relief” as employed. fortheeconomytorebuildthelostcapital. Finally,Figure6plotsseveralestimatesofunemploymentratebetween1929and1940(thelast year in the model that is treated as unaffected by the economic activity associated with WWII), sourced from the NBER–Conference Board, Lebergott (1964) and Darby (1975). Despite some differences caused in part by varying definitions of the unemployed, all three series indicate a sharp increase in unemployment of about 20 percentage points between 1929 and 1932.26 After that, with the exception of 1938, all three series slowly converge to their long-run rate of about 4 percent (calculated for the period 1945 to 1950). Table 3 displays the deviations (in percentage points)inunemploymentratesfromtheirinitialsteadystatelevelthroughouttheGreatDepression that we derive from the Conference Board data and incorporate in the model. Similar to TFP, we do not want to incorporate the decrease in the unemployment rates that are due to WWII, so we assumetheshockstotheunemploymentratesfrom1941-1945linearlydeclinetozero. 26OnereasonwhyLebergott’sandDarby’sseriesdivergeinlateryearsisthatLebergott(1964)considersindividuals in “work relief” programs as unemployed while Lebergott (1964) considers these individuals employed. The ConferenceBoardseriesdoesnotreportwhethertheyincludeindividualsin“workrelief”programsasunemployed. SeeMargo(1993)foradescriptionofthedifferencesbetweensomeoftheseestimates. Ofnote,Lebergott’sseriesis basedonseasonallyadjustedmonthlyestimateswhichwethenconverttoannualestimatesbytakingtheaverageover theyear. 19

Table3: ShocktotheInitialSteadyStateUnemploymentRate(inPercentagePoints) Year Shock 1932 18.6%∗ 1933 19.3% 1934 15% 1935 13.5% 1936 10.2% 1937 8.1% 1938 14.3% 1939 12.3% 1940 10.5% 1941 8.4% 1942 6.3% 1943 4.2% 1944 2.1% 1945 0% Notes: Shockrepresentsincreaseintheunemploymentrate, inpercentagepoints, duetotheeconomicdownturn. * Denotes an unexpected shock to the unemployment rate, all subsequent changes in the unemployment rate are not unexpected. To avoid the boost to economic activity from WWII, for 1941-1945, the deviations are extrapolated assumingthattheshockrecedesinalinearmanneroverthisperiod. 5.2 Social Security Social Security was initially signed into law amidst the Great Depression in late 1935. According to the original law, all eligible agents were scheduled to start funding the system in 1937, with the first benefits payments being paid out in 1942. However, the 1939 amendments introduced three notable changes: (i) the program became more inclusive, (ii) eligible agents were allowed to receive benefit payments already in January 1940 (i.e., two years ahead of the initial schedule), and (iii) income earned by agents after reaching the NRA was included in the calculation of the Social Security benefits (bss). For computational tractability, we assume that agents learn about both the original law and these later amendments at the end of 1935.27 Second, we ignore further amendmentsafter1940whichwerenotpartoftheinitialprogramthatwasimplemented. During the initial phase-in, the program differed from the its steady state version in several important ways. First, unlike in the steady state where all agents were eligible to collect Social 27Therefore, priorto1936agentsareunawarethattheprogramwillbeenactedandactasiftheprogramwillnot exist. 20

Table4: SocialSecurityTaxRates Year PayrollTaxRate 1937 2.0% 1938 2.0% 1939 2.0% 1940 2.0% 1941 2.0% 1942 2.0% 1943 4.0% 1944 4.0% 1945 4.0% Notes: The payroll tax rates from 1937 through 1945 are equal to their historical values. After 1945 they are set at 4.5%,consistentwiththeratethatclearstheSocialSecuritybudgetconstraintinthesteadystate. Security after retirement because they paid into the system, not all agents in the original cohort were eligible for Social Security benefits. In particular, along the transition, agents who never contributed payroll taxes were ineligible for Social Security.28 Second, in accordance with the historical experience, we let the payroll tax rate vary along the transition path. In particular, we set the 1940-1945 rates equal to their historical levels (see Table 4). However, after 1945, we set τss =0.045, the rate at which the Social Security program’s budget is balanced in the final steady state.29 Third, and most important for the welfare implications, benefits were calculated from the average lifetime earnings only after the program was adopted.30 Thus, along the transition equation2isalteredto: min{y ,y}+(j−1−19−s)x j j x = , (10) j+1 j−19−s wheresistheagent’sagein1937. 28Onexceptiontothisgeneralrulewereagentswhoturned65between1937and1940. TheseagentspaidSocial Securitytaxesuntiltheyturned65,butdidnotqualifyforthestandardretirementbenefitcalculationasdescribedin Section 2.4. Instead, these agents were reimbursed 175% of the amount they contributed in payroll taxes in a lump sumpayout. Thisexceptionisincorporatedintoourmodel. 29In reality, the actual rate hovered around a slightly higher level of about 5 percent over this period. However, someofthisrevenuewasusedtofundotherpartsoftheSocialSecurityprogramthatwerenotrelatedtotheretirement benefits,suggestingthatourcalibrationlikelyrepresentsareasonableapproximationoftheworldatthetime. 30Thismodifiedformulaisconsistentwiththeactualformula. 21

6 Results 6.1 Welfare Effects of Social Security in the Steady State This section compares the steady state economies without Social Security (the initial steady state) and with Social Security (the final steady state). Table 5 shows the aggregate variables in each economy while Figure 7 depicts the life cycle profiles. As shown Panel B of Figure 7 and in Table 5, the average savings profile as well as the level of aggregate capital K is lower in the final steady state. This is because, in the steady state with Social Security, agents only finance part of their post-retirement consumption from private funds, as some is financed with Social Security benefits. The lower K, paired with the aggregate labor supply N that is only marginally lower, translates into a higher return to capital r and lower market wage w. In turn, the higher return r in the steady state with Social Security affects the inter-temporal allocation of consumption and leisure, inducing agents to consume less and to enjoy less leisure early in life (Panels A and C of Figure 7). Finally, in the steady state with Social Security, agents retire, on average, 10 years earlierthaninthesteadystatewithoutSocialSecurity. Table5: AggregatesintheSteadyStates Aggregate NoS.S. WithS.S. Y 0.86 0.83 K 2.6 2.38 N 0.47 0.46 w 1.19 1.16 r 0.05 0.06 tr 0.07 0.05 τss 0 0.04 Avg. RetirementAge 76.7 64.3 Table 6 shows the expected average welfare change for agents from being born into the steady state with Social Security versus the steady state without Social Security, measured in consumption equivalent variation (CEV). Consistent with the existing studies, Table 6 confirms that Social Security is associated with lower long-run welfare. In particular, newborn agents in the steady stateeconomywithSocialSecuritywouldbewillingtogiveupapproximately4.7percentoftheir expectedfutureper-periodconsumptioninordertobebornintoaneconomywithoutSocialSecu- 22

Figure7: LifeCycleProfilesinSteadyState A: Consumption Profiles in Steady States 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.220 30 40 50 60 70 80 90 100 noitpmusnoC B: Savings Profiles in Steady States 8 6 4 No S.S. 2 With S.S. 0 20 40 60 80 100 Age htlaeW No S.S. With S.S. Age C: Labor Profiles in Steady States 0.4 0.3 0.2 0.1 0 20 40 60 80 100 robaL No S.S. With S.S. Age Note: “No S.S.” denotes the steady state without Social Security. “With S.S.” denotes the steady state with Social Security. rity. Moreover, the likelihood that a newborn agent experiences more welfare in the steady state withSocialSecurityrelativetothesteadystatewithoutitisonlya0.5percent.31 The channels associated with the reduced welfare are standard. The program affects welfare both through direct channels and also through general equilibrium effects. With regards to the direct effects, Social Security provides both inter- and intra-generational insurance. These potential effects are partly offset by two channels. First, the payroll tax makes it harder for younger and low-wageagentstoearnenoughafter-taxincometoaccumulateprecautionarysavingsandsmooth consumption. Inaddition,theprogressivecontribution-benefitsformuladistortsagents’laborsup- 31Thatsaid,thereductioninwelfareduetothepresenceoftheoriginalprogramissubstantiallylowerthanthatassociatedwiththecurrentSocialSecurity,largelybecausetheoriginalprogramwasmuchsmaller.PetermanandSommer (2014)estimatewelfarelossesfromthecurrentprogramofabout13percent. HongandR`ıos-Rull(2007),Storesletten et al. (1998) and Imrohoroglu et al. (2003) report ex-ante welfare losses from the current program between 3.7 percentand12.9percent–somewhatsmallerthanthoseestimatedinPetermanandSommer(2014). UnlikePetermanand Sommer(2014)andthispaper,thosepapersgenerallydonotsimultaneouslyincludeendogenouslabor,endogenous retirement,andidiosyncraticlaborproductivity,unemploymentandmortalityrisk. 23

Table6: DecompositionofSteadyStateWelfareEffectsfromSocialSecurity ContributionFrom: TotalEffect DirectEffects G.E.Effects Welfare(CEV) -4.7% -0.5% -4.3% Note: CEV measures the uniform change in expected per-period consumption that an agent would require to be indifferent between living in an economy without Social Security and an economy with Social Security. The direct effectsaredeterminedbycomparingthewelfareofagentsbornintothesteadystatewithoutSocialSecurityandwith Social Security, holding factor prices constant at the levels of the steady state without Social Security. The general equilibriumeffectiscalculatedasadifferencebetweentheoverallanddirecteffects. ply decisions. With regards to the general equilibrium effects, the program “crowds-out” private savings,therebyreducingthestockofaggregatecapital,whichaffectsthemarginalproductofboth capitalandlaborinthegeneralequilibrium. Wenextdecomposetheoverallsteadystatewelfarelossintoeffectsthataretransmittedthrough the direct vs. general equilibrium channels. The direct effects are determined by comparing the welfareofagentsbornintothesteadystatewithoutSocialSecurityandwithSocialSecurity,holding factor prices constant at the levels of the steady state without Social Security. The general equilibriumeffectiscalculatedasadifferencebetweentheoverallanddirecteffects. We find that the direct effects from Social Security decrease welfare by 0.5 percent of CEV, indicating that—at least for the original program—the positive welfare effects from the insurance are smaller than the negative welfare effects from the distortions on agents’ decisions and from theadverseeffectofpayrolltaxesonbudgetconstraints. Thegeneralequilibriumeffectsaremuch stronger,leadingtoanadditionalreductioninwelfareof4.3percentofCEV,accountingforalmost 90percentofthetotalwelfareloss. 6.2 Welfare Effects of Social Security During Transition InordertoassessthewelfareeffectsofadoptingSocialSecurityfortheoriginalcohorts,wecalculate two separate transition paths. First, we simulate the baseline transition from the initial steady state without Social Security to the final steady state with Social Security along which the Great Depression happens. Second, we simulate a counterfactual transition in which Social Security is notadopted,buttheGreatDepressionstilloccurs. Comparingthewelfareofagentsbetweenthese 24

Figure8: PredictedFluctuationsversusActualFluctuations A: Ouptut 110 100 90 80 70 60 50 St. St. 1932 1933 1934 1935 1936 1937 1938 1939 1940 xednI B: Wealth 110 Model Prediction 100 Data 90 80 70 60 S 5 t 0 . St. 1932 1933 1934 1935 1936 1937 1938 1939 1940 Year xednI Model Prediction Data Year C: Labor 110 100 90 80 70 60 50 40 St. St. 1932 1933 1934 1935 1936 1937 1938 1939 1940 xednI Model Prediction Data Year Note: Theblacklinescapturethesimulatedchangesineconomicaggregatesalongthetransitionpathrelativetotheir original values in the steady state without Social Security. The dashed red lines capture the actual changes in the aggregateeconomicvariablesrelativetotheirtrend. Thetrendsarecalculatedusingasecondorderpolynomialusing datafrom1900through1929. Allvaluesareindexedto100in1929,whichisconsideredthesteadystate. Allthree historicaldataseriescomesfromKendricketal.(1961). twotransitionpathspinsdownthewelfareeffectsfromadoptingSocialSecurity. Figure8showshowcloselyfluctuationsinaggregateoutput,wealth,andlaborinbaselinetransition (which includes the historical events of the Great Depression and the subsequent adoption of Social Security) match the fluctuations in the actual data.32 Overall, the model does a good job predicting the actual fluctuations in output and wealth. However, the model underpredicts the fluctuationsinlabor.33 Next,Figure9comparestheevolutionofmacroeconomicaggregatesalong thebaselineandcounterfactualtransitionpaths. (AppendixBdiscussesthesedynamicsindetails.) We use two welfare metrics to gauge the welfare effects from adopting Social Security for the 32Weendthecomparisonin1940sinceby1940thewarbuild-upmaypotentiallyhavebeguntoaffecttheseaggregates. 33The underprediction from the model may be due to the model not incorporating underemployment during the GreatDepression. Assuch,themodelmayunderpredictthetotalharmfromtheGreatDepression. 25

Figure9: AggregateFluctuationsOverTransition A: Output 10 0 −10 −20 −30 −40 0 20 40 60 80 100 120 .tS.tS lanigirO morf noitaiveD % B: Capital 0 −10 −20 Baseline Transition −30 Counterfactual Transition −40 0 20 40 60 80 100 120 Time after Initial Shock (1932) .tS.tS lanigirO morf noitaiveD % C: Labor 10 5 0 −5 Baseline Transition −10 Counterfactual Transition −15 0 20 40 60 80 100 120 Time after Initial Shock (1932) .tS.tS lanigirO morf noitaiveD % Baseline Transition Counterfactual Transition Time after Initial Shock (1932) D: Hours 10 5 0 −5 −10 −15 0 20 40 60 80 100 120 .tS.tS lanigirO morf noitaiveD % E: Consumption 5 0 −5 −10 −15 −20 Baseline Transition Counterfactual Transition −25 −30 0 20 40 60 80 100 120 Time after Initial Shock (1932) .tS.tS lanigirO morf noitaiveD % F: Rental Rate 60 40 20 0 Baseline Transition −20 Counterfactual Transition −40 0 20 40 60 80 100 120 Time after Initial Shock (1932) .tS.tS lanigirO morf noitaiveD % Baseline Transition Counterfactual Transition Time after Initial Shock (1932) G: Wage 5 0 −5 −10 −15 −20 −25 −30 0 20 40 60 80 100 120 .tS.tS lanigirO morf noitaiveD % Baseline Transition Counterfactual Transition Time after Initial Shock (1932) Note: Theblacklinescapturethepercentchangesineconomicaggregatesalongthebaselinetransitionpathfromthe originalsteadystatewithoutSocialSecuritytothenewsteadystatewithSocialSecurityduringtheGreatDepression. The blue dashed lines capture the percent changes in economic aggregates along the counterfactual transition path fromtheoriginalsteadystatewithoutSocialSecuritytotheGreatDepressionwithouttheadoptionofSocialSecurity. 26

Table7: DecompositionofTransitionalWelfareEffectsfromSocialSecurity ContributionFrom: TotalEffect DirectEffects G.E.Effects GreatDepression CEVtrans 3.5% 5.7% -0.9% -1.2% Note: AllwelfareeffectsarecalculatedasthedifferenceinthewelfareforagentslivinginaneconomywhereSocial SecurityisadoptedandwhereSocialSecurityisnotadopted. Thetotaleffectcapturestheaveragewelfaregainacross alllivingcohorts. TheGreatDepressioneffectsarecalculatedasthedifferencebetweenthetotalwelfareeffectswhen the Great Depression is included and the welfare effects in simulations when the Great Depression is not included. ThedirecteffectiscalculatedasthewelfareeffectinsimulationswheretheGreatDepressioniseliminatedandfactor pricesareheldconstantattheirinitialsteadystatelevelsthroughoutthetransition. Thegeneralequilibriumeffectsare calculatedinsimulationsthatexcludetheGreatDepression. Inparticulartheyarecalculatedasthedifferenceinthe welfareeffectswhenfactorpricesareallowedtofluctuateandwhentheyareheldconstantattheirinitialsteadystate levels. original cohorts. First, we calculate the ex-post likelihood that an agent will experience greater total lifetime utility in the benchmark transition in which Social Security is adopted than in the counterfactual transition in which Social Security is not adopted. We refer to this likelihood as Πtrans,anddefineitas: (cid:104) J−j J−j (cid:105) Πtrans U (cid:0) cB,hB(cid:1) + ∑βsU (cid:0) cB ,hB (cid:1) >U (cid:0) cC,hC(cid:1) + ∑βsU (cid:0) cC ,hC (cid:1) , (11) j j j+s j+s j j j+s j+s s=1 s=1 with cB and cC denoting the per-period consumption levels in the benchmark transition and the j j counterfactual transition, respectively. Second, we define transitional CEV (or CEVtrans) as the uniformpercentincreaseinexpectedconsumptionineachperiodovertheremainderofanagent’s lifetime that makes the agent indifferent between experiencing the benchmark and the counterfactualtransitions: E (cid:2) U (cid:0) cB,hB(cid:1) +∑ J−j βsU (cid:0) cB ,hB (cid:1)(cid:3) =E (cid:2) U (cid:0) (1+CEVtrans )cC,hC(cid:1) +∑ J−j βsU (cid:0) (1+CEVtrans )cC ,hC (cid:1)(cid:3) . j j s=1 j+s j+s 100 j j s=1 100 j+s j+s (12) A positive CEVtrans implies a welfare gain from the program’s adoption. When examining the welfare effects for specific cohorts, we index living cohorts by their age at the time when Social Securityisannounced,andfuturecohortsbythenumberofyearsaftertheannouncementthatthey entertheeconomy. 27

Figure10: EffectofGradualImplementation 120 100 80 60 40 20 0 20 40 60 80 etatS ydaetS fo % Benefits Received Taxes Paid Age at Time of Announcement Note: ThevaluesindicatetheaveragepercenteachagentpaysintoandreceivesfromSocialSecuritycomparedtothe value the respective values if these agents lived in the steady state with Social Security. The values are the average withinacohort. Table 7 shows CEVtrans for the original living cohorts.34 In contrast to the welfare effects of Social Security in the steady state, we estimate that the adoption of the original Social Security program led to large welfare gains among the original living cohorts. In particular, the average expectedwelfaregainfromSocialSecurityforagentsintheeconomyatthetimeofannouncement is the equivalent of 3.5 percent of expected future consumption, compared to a welfare loss in the steady state. Moreover, the likelihood that these agents gain welfare from the adoption of Social Security(Πtrans)isestimatedat73.7percent,comparedtomere0.5percentinthesteadystate. In the steady state, we decomposed the average welfare effect into two subcomponents: the welfare effect that is transmitted through general equilibrium vs. direct channels. We conduct a similar decomposition for the transitional welfare effects; however, we isolate the welfare effects oftheGreatDepressionintoitsownseparatecategory(seethelegendinTable7fordetailsonhow we do this). Column (2) shows that, unlike in the steady state, the direct equilibrium effects are associatedwithlargewelfaregainsfortheoriginalcohorts. Theprimaryreasonforthisdifference is the relatively faster speed at which Social Security benefits were phased in compared to the contributions. To illustrate this, the solid and dashed lines in Figure 10 plot the average lifetime Social Security benefits received and taxes paid by living cohorts in the benchmark transition 34The economy-wide average of the transitional welfare effects is calculated as the population-weighted average acrosscohorts. 28

Figure11: SocialSecurityOutlaysandRevenues A: Outlays and Revenues 100 80 60 40 20 0 20 40 60 80 etatS ydaetS fo % B: Coverage Ratio 20 15 Social Security Revenue 10 Social Security Payments 5 0 20 40 60 80 Years after Announcement oitaR Years after Announcement Note:Thevaluesarethetotaloutlaysorrevenuesreceivedinaparticularyear. Thevaluesarenormalizedasapercent ofthetotaloutlaysandrevenuesreceivedinthesteadystatewithSocialSecurity. Outlayequalrevenuesinthissteady state. Therightpanelistheratioofagentspayingpayrolltaxestothenumberofagentsreceivingbenefits. (expressedasafractionoftheirfinalsteadystatevalues),respectively. Thedifferencebetweenthe two lines demonstrates that most agents in the economy during the transition received far more benefits relative to their Social Security contributions than what they would have had they lived theirentirelifeinthesteadystatewithSocialSecurity. TheoriginalcohortscontributedrelativelylessintotheSocialSecuritysystemfortworeasons. First, the payroll tax rates were initially introduced at the low level of 2 percent (less than half of the steady state level), and stayed low for a number of years. Second, the original cohorts did not start paying into the system until the program was adopted, part way through their life. In contrast,thebenefitswerefullyimplementedimmediately,thoughthescalingfactorbasedonyears of employment somewhat lowered the benefits for the transitional agents because these agents did not pay as many years into the system. Overall, this implies that the Social Security benefits were onnetmoregenerousrelativetoagents’contributionsduringthetransition. Althoughtheprogramisstructuredsuchthatthetaxesaremoregraduallyimplementedthanthe benefits, we find that the program does not run a deficit. The left panel in Figure 11 plots the total outlaysandrevenuesforSocialSecurityineachyearaftertheprogramisannounced. Wefindthat in all periods revenues either equal or exceed outlays, largely because the number of individuals contributingpayrolltaxesexceedsthenumberofSocialSecuritybeneficiariesinagivenperiodby roughlyafactorof10(rightpanelinFigure11).35 35Similarly,through1960annualtotalexpendituresfromtheOldAgeSurvivorshipDisabilityInsurance(OASDI) 29

Column (3) shows that, similar to the steady state, the general equilibrium effects have a negative contribution to the overall welfare effects because the program crowds out capital. However, along the transition, this effect is much smaller because it takes many periods for agents to adjust their savings levels in response to the program’s adoption, so the crowd out of capital takes a long periodoftimetobefullyrealized(seeFigure9). Thus,alongthetransition,thegeneralequilibrium effectmerelymutestheoverallwelfaregainfromtheprogram’sadoptionfortheoriginalcohorts. Perhaps surprisingly, Column (4) demonstrates that adopting the program during the Great Depression tapered the potential overall welfare benefit from adopting the program. This result may seem counterintuitive since the old-age consumption insurance that Social Security provides would seem to be more beneficial in the midst of the Great Depression when large amounts of wealth and income were lost. However, while the adoption of Social Security during the Great Depression increased the welfare gains from the program’s adoption for some (generally older) agents relative to its adoption during “normal times,” adopting Social Security during the Great Depression exacerbated welfare losses caused by the economic downturn for most agents. These agents did not receive Social Security payments for many years to come, but had to start funding thesystemimmediately,atatimewheneconomicconditionswereespeciallyweak. 6.3 Welfare Effects by Age Next, we examine how the welfare effects from adopting Social Security vary by the agent’s age at the time of the announcement. We separate the agents into three groups: (i) agents eligible for Social Security that are in the model at the time of the announcement, (ii) agents ineligible for Social Security that are in the model at the time of the announcement (because they had already retired),(iii)agentswhohavenotenteredthemodelatthetimeoftheannouncement.36 trust fund were less than annual revenues. However, making this comparison in the data and the model is not completelyequivalentfortworeasons. First,bothrevenuesandexpendituresinthedataincludepartsofOASDIotherthan justtheold-ageconsumptioninsurance. Second,furtheramendmentsofSocialSecuritymadetheprogramlarger. The larger size of benefits relative to the original program modeled here induces earlier retirement, thereby reducing the fractionofcoveredworkerstobeneficiaries. 36Agentsenterthemodelattheageof20. Therefore,thisthirdgroupincludesagentsundertheageoftwentyatthe timethattheprogramisannouncedandagentsyettobeborn. 30

Figure12: WelfareEffectforEligibleAgentsfromImplementingSocialSecuritybyAge A: Likelihood of Welfare Gain 100 80 60 40 20 0 20 40 60 80 )%( doohilekiL B: Welfare Gain 20 15 10 5 0 20 40 60 80 Age at Time of Announcement )%( VEC Age at Time of Announcement Note: ThevaluesaretheaveragewithineachcohortforagentsthatareeligibletoreceiveSocialSecuritybenefits. 6.3.1 EligibleAgents We start by focusing on the welfare effects from the adoption of Social Security for agents in the model who were eligible for Social Security benefits at some point in their lifetimes: over 90 percent of all agents alive at the time of the program’s announcement. The fraction of agents eligible for Social Security is high for two main reasons. First, the fraction of the population eligible was largely determined by the share of agents who worked at the time of the program’s announcement. Prior to the adoption of Social Security, many worked until advanced ages and some (especially lower-income agents) worked until they died.37 Second, the Great Depression causedsomeagentstofurtherdelaytheirretirementtomakeupforthelostwealthandincome. TheleftpanelinFigure12plotseacheligiblecohort’slikelihoodofgainingwelfareduetothe implementation of Social Security. Perhaps not surprisingly, the likelihood of welfare gains rises with the cohort’s age at the time of the program announcement. In particular, the likelihood of an increase in welfare due to the adoption of the program is only 60 percent for households age 20 at the time of the program’s announcement, whereas the likelihood increases to close to 100 for households ages 40+. The likelihood of gains rises for two reasons. First, individuals who are younger at the time of the program’s announcement are more likely to be adversely affected by the payroll taxes because they tend to be more liquidity constrained. Second, the older an agent was at the time of the program’s adoption the fewer years of payroll taxes the agent contributed 37In the initial steady state without Social Security, the average age of death (conditional on agent’s surviving through age 20) is 66 in the model, whereas the average retirement age (for agents who do not die prior to them retiring)is76inthemodel. 31

priortoreceivingSocialSecuritybenefits. Whilefeweryearsofcontributedpayrolltaxeslowerthe post-retirementbenefitsize,thisreductioninbenefitsisrelativelysmallerthanthedecreaseintotal payroll tax liability, meaning that essentially all eligible agents in age cohorts 40+ enjoyed higher welfare due to the adoption of the program. For example, an agent who retired five years after the inception of Social Security would face a lifetime payroll tax burden that was approximately 95 percent lower than that of the same agent who paid payroll taxes throughout their entire working lifetime.38 Yet, despite paying considerably less payroll taxes, this agent would be entitled to a SocialSecuritybenefitthatwasonly40percentlower.39 Therightpanelshowseachcohort’sexpectedex-antegainfromtheadoptionofSocialSecurity (CEVtrans). Similar to the left panel, the profile rises for all cohort. However, unlike in the left panel, the speed of the increase in theCEVtrans slows temporarily for cohorts age 62 to 70. What causes the CEVtrans to rise less rapidly for cohorts in this particular age range? To understand these dynamics, one has to examine the composition of the welfare effects from the program by agents’wealthandage. The upper left panel of Figure 13 plots the CEVtrans by age for each quintile of the wealth distribution.40 After age 62, the welfare gains from the adoption of Social Security decline for agents in the top two quintiles. In contrast, the welfare gains continue to rise or hold steady for cohorts ages 62+ in the lowest three quintile. Since the higher-wealth agents tend to retire earlier, eligible cohorts ages 70+ are disproportionately made up by low-wealth agents (Panel C in Figure 13). Hence, among cohorts who are in their sixties at the program’s announcement, the fractionofwealthyagents,whoseCEVtrans decreaseswithage,islargeenoughtocauseaslowing in the increase in the aggregateCEVtrans. However, among cohorts who are in their seventies, the lower wealth quintile makes up a large enough fraction of the eligible agents in these cohorts so thattheCEVtrans riseatanincreasingspeed. 38Thistaxburdenwouldbereducedfortworeasons. First,theagentwouldonlypaypayrolltaxesforfiveyears,as opposedto45yearsiftheylivedinthesteadystate. Second,thepayrolltaxratesbeganatamuchlowerrateandwere phasedinoveranumberofyears. 39The40percentreductionrepresentstheagentpayingintothesystemfor40lessyearsandthusreceivingascaleup factorofonly5percentasopposedto45percent. Fortheconvenienceofexpositionofthisargument,inthisexample weassumethatanagent’sincomewasconstantacrosshisworkinglifecycle,thediscountrateisone,andtheagent retiresatage65. 40Thewealthquintilesaredeterminedforeachagentbycomparingthetotalwealthatthetimeoftheannouncement ofSocialSecuritywithineachcohort. 32

Figure13: EffectbyAgeandWealth A: Welfare Gain (by wealth) 25 20 15 10 5 0 30 40 50 60 70 80 )%( VEC B: Percent of Agents Eligible (by wealth) Q1 100 Q2 80 Q3 Q4 60 Q5 40 20 0 30 40 50 60 70 80 Age at Time of Announcement noitalupoP fo tnecreP Q1 Q2 Q3 Q4 Q5 Age at Time of Announcement C: Ratio of Benefits to Taxes 100 80 60 40 20 0 30 40 50 60 70 80 VPN fo oitaR D: Avg. Yrs. Worked after Eligible 5 Q1 Q2 4 Q3 Q4 3 Q5 2 1 0 65 70 75 80 Age at Time of Announcement sraeY Q1 Q2 Q3 Q4 Q5 Age at Time of Announcement Note: TheupperleftpanelplotsthewelfaregainintermsofCEVbyageandwealthquintile. Theupperrightpanel describesthepercentofagentswhoareeventuallyeligibletoreceivebenefits. Thelowerleftpanelplotstheratioof thenetpresentvalueofthelifetimebenefitsreceivedfromtheprogramrelativetothelifetimepayrolltaxespaid. The lowerrightpaneldescribesthenumberofyearsagentsworkafterbecomingeligibletostartreceivingSocialSecurity benefits. 33

The different dynamics of the CEVtrans by age for the different wealth quintiles can be explained by the relative size of the total benefits received compared to the total payroll taxes paid. The lower left panel in Figure 13 plots the discounted net present value (NPV) of the ratio of the expected benefits to payroll taxes for these agents by wealth quintile. For the bottom wealth quintile, the NPV benefits-contribution ratio rises monotonically with age at the time of the adoption. In contrast, for the top wealth quintiles, the ratio peaks round age 62 and subsequently falls for agentsolderatthetimeoftheadoption. Why does the NPV benefits-contribution ratio rise for the bottom wealth quintiles even as it falls for the top quintile? The different dynamics are primarily driven by the differences in retirement decisions across wealth quintiles. The lower left panel in Figure 13 plots the average number of years that a transitional agent works after becoming eligible to collect Social Security benefits by wealth quintile. Irrespective of their age at the time of the program’s announcement, agents in the top wealth quintile generally retire immediately after becoming eligible for benefits (i.e.,aftercontributingthreeyearsofpayrolltaxes).41 Asaresult,theNPVoftheseagents’Social Securitycontributionsisquitesimilarirrespectiveoftheirageattheannouncement. Incontrast,the NVPofthetotalbenefitreceiveddeclinestheolderanagentisatthetimeoftheprogram’sadoption due to rising mortality risk.42 Thus, the overall welfare gain for these high-wealth individuals’ decreases the older an agent is at the time of the program’s adoption. In a marked contrast, for low-wealth agents, the number of years that a transitional agent works after becoming eligible to collectbenefitsdeclineswiththeagent’sageatthetimeoftheprogram’sadoption. Fortheseolder low-wealth agents, the NPV of the benefits-contribution ratio tends to rise because the ratio of expectedyearsreceivingSocialSecuritybenefitsvs. contributingpayrolltaxesriseswiththeirage atthetimeoftheprogram’sannouncement. 6.3.2 IneligibleAgents This section focuses on the welfare effects of the program’s adoption on agents who are alive at the time of the program’s enactment but are already retired and, therefore, ineligible to collect 41Thesethree yearsare fromthe beginningof thetaxes beingcollectedin 1937until benefitsbegin beingpaid in 1940. 42ThedeclineintheNPVisbecausetheolderanagentis,inexpectation,thefeweryearshehastoliveandtocollect thebenefits. Moreover,onaverageolderagentsreceivelowerwagescausingtheeventuallySocialSecuritypayment tobeloweratthetimeofretirement. 34

Figure14: WelfareGainfromImplementingSocialSecurityForIneligibleCohorts A: Likelihood of Welfare Gain 100 80 60 40 20 0 60 70 80 90 )%( doohilekiL B: Welfare Gain 0.5 0 −0.5 60 70 80 90 Age at Time of Announcement )%( VEC Age at Time of Announcement Note: ThevaluesaretheaveragewithineachcohortforagentsthatareeligibletoreceiveSocialSecuritybenefits. benefits: less than 10 percent of the living population. Figure 14 shows that the welfare effects of the program’s adoption on these agents are overall small and largely depend on these agents’ age when the program is announced. In particular, for ineligible agents ages <80, the program’s adoptionisgenerallyassociatedwithasmallreductioninwelfare,comparedtoasmallincreasein welfareforagentsages80+.43 Through which channels are ineligible agents affected? Given that these agents are already retired, they are not affected by the direct effects from Social Security nor are they affected by the relativedynamicsofthewagerate. Instead,thedrivingfactorbehindthemeasuredwelfareeffects is the relative change in the rental rate between the benchmark and counterfactual transitions, showninFigure15. Thefigureshowsthattherelativereturntosavingsrisesbutsubsequentlydips for a few periods in the benchmark transition in which Social Security is implemented compared to the counterfactual transition in which it is not. The relatively higher rental rate following the program’s announcement causes the small welfare gain for the ineligible agents ages 80+. These agents benefit from the increase in the return to savings, but generally do not live long enough to also experience its subsequent decline. In contrast, the subsequent dip in the relative rental rate causes the small welfare loss for ineligible agents ages <80 for whom the negative welfare effect of the experienced relative decline in the interest rate more than offsets the positive effect of its 43Thereisakinkinthewelfareeffectsforage80cohorts. Thiskinkarisesbecausethecompositionofineligible agentsisdifferentforcohortswhowereunder80atthetimeoftheadoptionversusoldercohorts. Inparticular,since agentswithhigherincomestendtoretireearlier(seebottomleftpanelofFigure13),theymakeuparelativelylarger fractionoftheineligibleagentsincohortsunder80. Moreover,thesehigherincomeagentstendtobenefitmorefrom thehigherrentalrate. 35

Figure15: FluctuationsinRentalRateduetoSocialSecurity 4 2 0 −2 −4 5 10 15 20 noitaiveD % Time after Announcement Note: The figures represent the percent difference in the rental rate between the transition with Social Security and thecounterfactualtransitionwithoutSocialSecurity. initialrelativeincrease.44 The higher rental rate in the baseline transition relative to the counterfactual transition followingtheprogram’sannouncementiscausedbyanincreaseintherelativeamountoflaborsupplied: whentheprogramisannounced,eligibleagentsworkmoreastheirlaborincomeisbeingcounted toward their future Social Security benefits. After this initial increase, two competing effects determine the subsequent dynamics of the relative rental rate. First, agents tend to retire earlier in the baseline transition when Social Security is adopted, thereby lowering the relative level of aggregate labor.45 Second, agents tend to hold relatively less savings in the baseline transition since theynolongerhavetofundalloftheirpost-retirementconsumptionwithprivatesavings. Thefirst effect initially dominates since agents’ labor supply decisions are more flexible, causing the temporary decrease in the relative rental rate. However, the de-accumulation of capital is eventually large enough that the second effect dominates in the long run and the rental rate in the baseline transitionreturnstoitsrelativelyhigheroriginallevel. 36

Figure16: WelfareGainfromImplementingSocialSecurityForFutureCohorts A: Likelihood of Welfare Gain 100 80 60 40 20 0 10 20 30 )%( doohilekiL B: Welfare Gain 0 −1 −2 −3 −4 −5 10 20 30 Years after Announcement Enter Economy )%( VEC Years after Announcement Enter Economy Note: Likelihoodofgainingwelfareiscalculatedasthepercentofthecohortwhoexperiencesawelfaregaindueto theimplementationofSocialSecurity.AgesinpanelAandBaretheageofagentswhenSocialSecurityisannounced. InpanelCthecohortsareindexedbythenumberofperiodsaftertheannouncementthattheyentertheeconomy(20 yearsold). 6.3.3 FutureCohorts Finally, we turn to agents who enter the model after the program is implemented. We find that agents who enter the model immediately after the implementation of Social Security on average expecttoexperienceawelfarelossfromtheprogram. Wefindthatthelikelihoodofawelfaregain for these agents is just slightly above forty percent and the expected welfare loss for these agents are around one percent of their expected lifetime consumption. As time passes, the likelihood of experiencing a welfare gain decreases for new entrants just as the size of the average expected welfare loss rises. This is because cohorts who enter the model many periods after the adoption of Social Security tend to pay relatively more in payroll taxes than agents who enter the model immediately after the announcement as the payroll tax rate is phased in only gradually over a period of ten years. Over time, both the likelihood of a welfare gain and the size of the average welfarelossestrendtowardstheirsteadystatevalues. 44Thesubsequentincreaseintherelativerentalratehaslimitedeffectonineligibleagentssinceittakesplacemore than15yearsaftertheprogramisannouncedwhentheseineligibleagentsareeitheralreadydeadorhaveverylittle savingssincetheywillonlyliveforafewmoreperiods. 45Earlyretirementdoesnotaffectaggregatelaborinthefirstfewperiodsaftertheprogramisannouncedbecause agentsmustworkuntil1940beforetheycanstartcollectingbenefits. 37

6.4 Sensitivity Analysis Finally, we determine the sensitivity of the results with respect to five dimensions. First, we computethewelfareeffectsunderthealternativeassumptionthatonlyagentsunderage65areeligible to receive Social Security benefits.46 Second, we compute the welfare effect under the alternative whereinSocialSecurityisadoptedimmediatelyattheonsetoftheGreatRecession,asopposedto in the midst of it. Third, we include a reduced-form unemployment insurance that replaces 35% percent of average earnings in the economy.47 Fourth, we determine the welfare effects if agents additionally face idiosyncratic i.i.d. shocks to the depreciation rate of their assets. Introducing these shocks means that retired agents not only hold savings to fund post-retirement consumption butalsoasaformofprecautionarysavingsagainstthesedepreciationshocks. Theshocksaresetat meanzerowithacoefficientofvariationequalto1.15,consistentwithKruegerandKubler(2006). Table 8 presents both the likelihood and average level of welfare gains for transitional agents in each of these sensitivity exercises. As in our baseline experiment, the welfare gains are derived from an experiment that compares welfare in the baseline transition in which both the Great Depression and the adoption of Social Security occur to the alternative transition in which the Great Depression takes place but Social Security is not adopted. Focusing on the third and fifth row, respectively,adoptingtheprogramattheonsetofthedepression,andincorporatingidiosyncraticrisk to the returns to savings both have only minimal effects on the welfare gains from Social Security fortransitionalagents. Onto the remaining experiments, when program eligibility is restricted to agents under 65 at the time the program is announced in the second row, the welfare gains are reduced relative to our baseline results, largely because fewer agents are eligible for the retirement benefits in this alternative experiment. In contrast, when unemployment insurance is included in the fourth row, the program becomes even more beneficial in welfare terms. When the baseline Social Security program is augmented with unemployment insurance, liquidity constraints are eased since agents no longer need to hold as much savings to insure against an unemployment shock. The easing of the liquidity constraints makes the negative distortions from the payroll tax less painful. Overall, 46Understandingtheeffectsofthisassumptionisrelevantbecausetheoriginallawexcludedagentsover65,however, theseagentswereincludedintheamendmentpassedin1939. 47Between1943and1960,theaveragereplacementrateforunemploymentinsuranceis35%.SeeTheEmployment andTrainingFinancialDataHandbook394ReportfromtheUnitedStatesDepartmentofLabor. 38

despitethesesmalldifferences,theoverallconclusionthatSocialSecuritytendstoincreasewelfare for agents alive when the program is adopted seems fairly robust to the alternative specifications consideredhere. Table8: SensitivityExercises CEV Likelihood Benchmark 3.5% 73.7% 65+Excluded 2.1% 71.3% ImmediateAdoption 4.0% 74.7% UnemploymentInsurance 7.8% 88.1% IdiosyncraticRisktoSavingsReturn 3.5% 73.4% 7 Conclusion ThispaperquantifiesthewelfareeffectsofSocialSecurityfortransitionalagentswhoexperienced theprogram’sadoption. Wefindthattheadoptionoftheprogrambenefitedavastmajorityofthese transitional agents. In particular, we estimate that the program benefited households alive at the time of the program’s adoption with a likelihood of over 70 percent, and increased these agents’ welfarebytheequivalentof3.5percentoftheirexpectedfuturelifetimeconsumption. Through a quantitative decomposition of the overall welfare effects, we find that the adoption of the program was largely beneficial because of the relative speeds at which the different parts of the program were phased in. In particular, the structure of the program’s phase-in was such that most transitional agents received far greater monetary benefits in a form of Social Security payments than the amount they contributed to the system through payroll taxes. Moreover, and perhaps interestingly, we find that adopting the program in the midst of the Great Depression had only a modest effect on the welfare implications of the program’s adoption and, if anything, reducedthewelfaregainsfromSocialSecurityforthetransitionalagents. Thispaperhighlightsthatthewelfareimplicationsforagentsalivewhentheprogramisadopted werequitedifferentthanthesteadystatewelfareeffects. Overall,thedivergentwelfarebenefitsfor agentswhoexperiencedtheprogram’senactmentversusthoseexperiencedbyagentsbornintothe steady state with Social Security might offer one explanation for why a program that potentially reduceswelfareinthesteadystatewasoriginallyadopted. 39

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A Equilibrium In this section we define a stationary steady state competitive equilibrium with Social Security.48 Anagent’sstatevariables,Ξareassets(a),averagepastearnings(x),age(j),ability(α),persistent shock (ν), unemployment shock (D), retirement status (I). For a given set of exogenous demographic parameters (n,Ψ ), a sequence of exogenous age-specific human capital ({θ }R ), govj j j=1 ernmenttaxfunction(T :R →R ),SocialSecuritytaxrateτss,SocialSecuritybenefitsformula + + (Bss :R × j→R ), a production plan for the firm (N,K), and a utility function (U :R ×R → + + + + R ), a steady state competitive equilibrium consists of agent’s decision rules for c,h,a, and I for + eachstatevariable,factorprices(w,r),transfers(Tr),andthedistributionofindividualsµ(Ξ)such thatthefollowingholds: 1. Given prices, policies, transfers, and initial conditions the agent solves the dynamic programmingprobleminequations4-7,withc,h,a(cid:48),andI asassociatedpolicyfunctions. 2. Thepricesw andr satisfy t t N r =ζA( t )1−ζ−δ t K t N w =(1−ζ)A( t )ζ. t K t 3. TheSocialSecuritypoliciessatisfy: ∑min{wDωh,y}τss µ(Ξ)=∑bss I µ(Ξ). 4. Transfersaregivenby: Tr=∑(1−Ψ )aµ(Ξ). j 5. Governmentbudgetbalance: G=∑Ty[r(a+Tr)+wDωh−.5τssmin{wDωh,y}]µ(Ξ)µ(Ξ). 48Condition3isnotrelevantinasteadystatewithnoSocialSecurity. 44

6. Marketclearing: K =∑aµ(Ξ), N =∑ωhµ(Ξ)and ∑cµ(Ξ)+∑aµ(Ξ)+G=AKζN1−ζ+(1−δ)K. 7. Thedistributionofµ(x)isstationary,thatis,thelawofmotionforthedistributionofindividualsoverthestatespacesatisfiesµ(x)=Q µ(x),whereQ isaone-periodrecursiveoperator µ µ onthedistribution. B Transitional Dynamics of Aggregates This section examines the benchmark transition of the economy from the steady state without Social Security to the new steady state with Social Security. Figure 9 plots the transition of output, capital, labor, hours, consumption, rental rate, and wage, respectively, over the transition. Even thoughby1945thebusinesscycleshocksdissipateandtheSocialSecurityprogramisfullyimplemented,theeconomydoesnotcompleteitstransitiontothenewsteadystateforapproximatelyan additional25years(i.e.,untiltheyear1970). Over the transition, aggregate output, aggregate capital, aggregate consumption, and the wage rate all fall drastically immediately upon the shock’s impact, continue to decline for a few extra periods, and then gradually transition back to their new steady state values. The remaining aggregates—labor, hours, and the rental rate—suffer two sharp declines over the transition before eventuallyendingupattheirnewsteadystatevalues. The fluctuations in the aggregate economic variables over the transition come from two channels: (i)theeconomicshocksassociatedwiththeGreatDepression,and(ii)theadoptionofSocial Security. Inordertodecomposethesetwoeffects,Figure17determinesthepercentagechangesin the aggregate economic variables relative to their initial values in the steady state without Social Security under three alternative transitions. First, the black lines plot the benchmark transition when the economy suffers the Great Depression and Social Security is implemented. The blue dashed lines plot the evolution of the aggregates in a counterfactual transition when the economy suffersthroughtheGreatDepressionbutSocialSecurityisnotadopted. Third,thereddashedlines describetheevolutionoftheaggregatesinasecondcounterfactualtransitionwhenSocialSecurity 45

isadoptedbutthereisnobusinesscycleepisode. Turning to Panels A, B, E, and G of Figure 17, the fluctuations in the benchmark transition (black line) and the transition which only includes the Great Depression (blue line) are similar for output, capital, consumption, and wages during the first 15 years of the transition. In these transitions, the initial declines in output, capital, consumption, and wages and the subsequent recovery are primarily caused by the shocks associated with the Great Depression. The subsequent fluctuationsintheseaggregatesinthebenchmarktransitionandthecounterfactualtransitionwhich onlyincludesthebusinesscyclefluctuationstendtodiverge. Theselaterfluctuationsareprimarily driven by the adoption of Social Security and not the shocks to savings, TFP, and the unemploymentrate. Turning to Panels C, D, and F, the transition of labor, hours, and the rental rate has multiple peaks and troughs. Comparing the fluctuations of these three aggregates over all three transitions, the original declines are primarily driven by the business cycle shocks. The initial fall in all three aggregates is due to the drop in TFP and increase in the unemployment rate,49 while the quick initial recoveries in these aggregates are due to the decline in the size of the shocks and also due to the implementation of Social Security (see the blue and red lines in Figure 17).50 In particular, as the unemployment rate declines and TFP increases, agents tend to increase their hours. Additionally, in these first few periods after Social Security is announced, older agents increase their future Social Security benefit by working more. Both of these factors drive up the aggregate labor supply and rental rate. However, these increases are short-lived, as the increase in the unemploymentrateinperiod7(1938)causesasecondfallinaggregatehours,aggregatelabor,andtherental rate. The second spike occurs in period fourteen. Since this spike is primarily due to the business cycle episode (the shocks to unemployment and TFP shocks finally recede), it does not occur in the counterfactual transition without the shocks (see the red line in Figure 17). After the second spikeinlabor,hours,andtherentalrate,allthreeaggregatesslowlydecreaseforanother25periods whentheyreachtheirnewsteadystatevalueswhicharelowerduetotheimplementationofSocial Security. 49Thefluctuationsintherentalrateareprimarilydrivenbythechangesintheratioofaggregatelabortooutput. 50Notethatunemploymenttemporarilydecreasesoverthisperiodbutincreasesagaininperiod7(1938). 46

Figure17: AggregateFluctuationsOverTransition A: Output 10 0 −10 −20 −30 −40 0 20 40 60 80 100 120 etatS ydaetS lanigirO morf noitaiveD % B: Capital 0 −10 −20 Recession and Social Security Recession Only −30 Social Security Only −40 0 20 40 60 80 100 120 Time after Initial Shock (1932) etatS ydaetS lanigirO morf noitaiveD % C: Labor 10 5 0 −5 Recession and Social Security Recession Only −10 Social Security Only −15 0 20 40 60 80 100 120 Time after Initial Shock (1932) etatS ydaetS lanigirO morf noitaiveD % Recession and Social Security Recession Only Social Security Only Time after Initial Shock (1932) D: Hours 10 5 0 −5 −10 −15 0 20 40 60 80 100 120 etatS ydaetS lanigirO morf noitaiveD % E: Consumption 5 0 −5 −10 −15 Recession and Social Security −20 Recession Only −25 Social Security Only −30 0 20 40 60 80 100 120 Time after Initial Shock (1932) etatS ydaetS lanigirO morf noitaiveD % F: Rental Rate 60 40 20 0 Recession and Social Security Recession Only −20 Social Security Only −40 0 20 40 60 80 100 120 Time after Initial Shock (1932) etatS ydaetS lanigirO morf noitaiveD % Recession and Social Security Recession Only Social Security Only Time after Initial Shock (1932) G: Wage 5 0 −5 −10 −15 −20 −25 −30 0 20 40 60 80 100 120 etatS ydaetS lanigirO morf noitaiveD % Recession and Social Security Recession Only Social Security Only Time after Initial Shock (1932) Note: Theblacklinescapturethechangesineconomicaggregatesalongthetransitionpathfromtheoriginalsteady state without Social Security to the new steady state with Social Security during the Great Depression. The red dashedlinescapturethechangesineconomicaggregatesalongthetransitionpathwhentheeconomysufferstheGreat Depression but Social Security is never implemented. The blue dashed lines capture the changes in the economic aggregatesalongthetransitionpathwhenSocialSecurityisadoptedbutthereisnoGreatDepression. Allthevalues arepercentagesrelativetheinitialvalueinthesteadystatewithoutSocialSecurity. 47